An improved hybrid ICA-SA metaheuristic for order acceptance and scheduling with time windows and sequence-dependent setup times

Order acceptance and scheduling (OAS) is a critical part of production planning in manufacturing units. In real-world problems, where the manufacturing units are required to meet capacity limitations and delivery time obligations, OAS problem arises. In this study, a hybrid population-based heuristic of imperialists competitive algorithm (ICA) and well-known simulated annealing (SA) has been applied to deal with the variant of OAS with time windows and sequence-dependent setup time. As part of ICA, a specific representation has been proposed to capture all of the characteristics of an OAS solution. The neighborhood functions have been developed based on this specific representation. In order to improve conventional ICA, a roulette wheel is used for selecting these functions, which is periodically updated based on their prior effectiveness. As an additional approach to avoid being confined to a local optimum point, an escape strategy is employed. This part of the study utilizes eight local search functions that are different from those in the ICA in order to further diversify the population. The proposed algorithm has been implemented on benchmark instances, and results have been analyzed. The results of our experiments demonstrated that ICA-SA shows improvement over well-known existing methods both in terms of quality and speed. In addition, we found in 32 out of 1500 cases, ICA-SA yielded a better result than the upper bound generated by MILP. This improvement in optimal solutions was made possible due to the allowance of scheduling tasks with zero revenue in this study. Therefore by relaxing one of the constraints of MILP, better upper bounds can be achieved.